Date on salaries in the public school system ere published amualy by a teachers\

Question

Date on salaries in the public school system ere published amualy by a teachers' associetion The mean annual salery of publc) classroom teachers is 156.1 thousand. Assume a standard deviation of $9.6 thousand. Complete parts (a) through (ej below a. Detarmne the sampling distibuton of the sample mean tor samples c size 64 The mean of the sample mean is -S . (Type an integer or a decimal Do not round) The standard deviation of the sample mean is ox . (Type an neger or a decrmal Do not round b. Determine the sampling distrbuton of the sample mean for samples ot size 256 The mean of the sample mean is -S . (Type an integer or a decimal Do not round) The standard deviation of the sample mean is ox-S .(Type an lie er or a deci al Do not round) c. Do you need to assume at classroom teacher saleres are normally distributed to answer parts(a) and (bI? Expiain your answer O A. No, because if x is normaly dsributed, then x must be normally distributed B. Yes, because x is oriy normaly distributed if x is normally distributed C. No, because the sample sizes are sufficiently large so thatxwill be approximately normaly distrbuled, regardess of he disribution of x. O D. Yes, because the sample sizes are not sufficienty large so thatx l be approximatey nomaly distributed regardless of the dsthbutionotx. d. What is the probability that the sampling error made in estmating he poptation mean salary of all classroom teachers by he mean sa ary or a sarple of 64 classroom teachers wil be at most $1000? (Round to three decimal places as needed.) e. Whet is the probability that the samping errer made in estimetng the popleton meen selary at al dassroom teachers by the meen salary of a sarpe of 258 clessrm eacherswill be at most S10D0? (Round to three decimal places as needed.)

Explanation / Answer

a)

sample mean ==population mean =56.1

std deviation of sample mean=std deviation/(n)1/2 =9.6/(64)1/2 =1.2
b)

sample mean ==population mean =56.1

std deviation of sample mean=std deviation/(n)1/2 =9.6/(256)1/2 =0.6

c) option C is correct

d)

e)

for normal distribution z score =(X-)/

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